Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 196, Issue 1, Pages 49-60Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2008.03.012
Keywords
Hausdorff metric; Hukuhara difference; H-Differentiability; Interval-valued function; KKT condition; Pareto optimal Solution
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The KKT conditions in multiobjective programming problems with interval-valued objective functions are derived in this paper. Many concepts of Pareto optimal solutions are proposed by considering two orderings on the class of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to define the distance between two closed intervals and the Hukuhara difference to define the difference of two closed intervals. Under these settings, we are able to consider the continuity and differentiability of an interval-valued function. The KKT optimality conditions can then be naturally elicited. (C) 2008 Elsevier B.V. All rights reserved.
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